Transcript ICPSR General Structural Equation Models

ICPSR General Structural
Equation Models
Week 4 # 3
Panel Data
(including Growth Curve Models)
Causal models:
1
Eta-1
Ksi-1
ga2,1
1
ga1,2
Ksi-2
Cross-lagged panel coefficients
[Reduced form of model on next slide]
Eta-2
Causal models:
1
Ksi-1
Eta-1
1
Ksi-2
Eta-2
Reciprocal effects, using lagged values to achieve model
identification
Causal models:
A variant
Issue: what does ga(1,1) mean given
concern over causal direction?
TV Use
gamma 1,1
Political
Trust
gamma2,1
Beta 2,1Pol
Trust
Time 2
Lagged and contemporaneous effects
This model is underidentified
1
1
Lagged effects model
Ksi-1 could be an “event”
1/0 dummy variable
ksi-1
ksi-2
eta-1
eta-2
First order model for three wave data
(univariate)
1
1
1
Time 1
1
1
1
1
1
1
1
1
Time 2
Time 3
1
First order model for three wave data
(univariate)
1
1
1
1
1
1
1
1
b1
Tests:
1
1
b1
Equivalent of stability coefficients (b1)
Mean differences (see earlier slide)
1
1
Second order model for three wave data
(univariate)
1
1
1
1
1
1
1
1
1
b1
No longer comparable to b1
(t1 t2)
b1
1
1
1
Second order model for three wave data
(univariate)
1
1
1
1
1
1
1
1
1
b1
b1
1
1
Issue: adding appropriate error terms (2nd order)
1
Multivariate Model for Three-wave panel
data: cross-lagged effects (first order)
1
1
1
1
Multivariate Model for Three-wave panel
data: cross-lagged effects (first order)
1
1
1
1
Equivalence of parameters:
T1  T2
T2  T3
Multivariate Model for Three-wave panel
data: cross-lagged effects (second order)
Multivariate Model for Four-wave panel data:
cross-lagged effects (second order)
Lagged and contemporaneous effects
Three wave model with constraints:
1
1
a
a
d
e
d
f
c
e
f
c
b
b
1
Under many circumstances, there will be an empirical
under-ident. problem, though in theory this model is
identified
1
Example:
• Canada, Quality of Life data
• In directory \Panel in
Week4Examples
Panel Data model
Model for attitudes about labour unions,
1977-1979
Items: 5-pt. agree/disagree
199D QD6B Unions too much power
Q156C QK16F Scabs (gov’t prohibit
strikebreakers)
Q156D QK16G Workers on Boards
Q156B QK16E Teachers should not have
right to strike
Source: Cdn. Quality of life panel study, 1977-1979 waves
1
Union atts
1979
Union Atts
1977
1
1
1
1
1
1
1
1
1
1
Panel Data model
LISREL Estimates (Maximum Likelihood)
LAMBDA-Y
Q199D
LABOR77
-------1.000
LABOR79
-------- -
Q156C
-1.803
(0.141)
-12.796
- -
Q156D
-1.148
(0.101)
-11.350
- -
Q156B
0.789
(0.098)
8.040
- -
QD7B
- -
1.000
QK16F
- -
-1.352
(0.109)
-12.355
QK16G
- -
-0.755
(0.072)
-10.479
QK16E
- -
0.709
(0.084)
8.427
Panel Data model
BETA
PSI
Note: This matrix is diagonal.
LABOR77 LABOR79
-------- -------0.125 -0.066
(0.017) (0.018)
7.529 -3.611
LABOR77
LABOR77
-------- -
LABOR79
Squared Multiple Correlations for Structural Equations
LABOR77 LABOR79
-------- --------1.356
W_A_R_N_I_N_G: PSI is not positive definite
1.420
(0.138)
10.318
LABOR79
-------- - -
Completely Standardized Solution
LAMBDA-Y
Q199D
Q156C
Q156D
Q156B
QD7B
QK16F
QK16G
QK16E
LABOR77
-------0.425
-0.559
-0.436
0.262
- - - - -
LABOR79
-------- - - - 0.409
-0.524
-0.382
0.277
BETA
LABOR77
LABOR79
LABOR77
-------- 1.165
LABOR79
-------- - -
Panel Data model
What is the problem
here?
Panel Data model
Theta-epsilon was specified as diagonal
Modification Indices for THETA-EPS
Q199D
Q156C
Q156D
Q156B
QD7B
QK16F
QK16G
QK16E
Q199D
-------- 2.845
3.439
17.009
83.881
10.361
19.366
0.158
Q156C
--------
Q156D
--------
Q156B
--------
QD7B
--------
QK16F
--------
- 20.324
5.334
42.939
108.940
28.336
7.133
- 13.004
10.988
28.775
141.658
14.031
- 4.108
23.541
5.494
169.430
- 2.034
0.242
25.246
- 7.172
6.019
Panel Data model
1
Union atts
1979
Union Atts
1977
1
1
1
1
1
1
1
1
1
1
Panel Data model
Added error covariances:
FR TE 5 1 TE 6 2 TE 7 3 TE 8 4
BETA
LABOR77
LABOR79
LABOR77
-------- -
LABOR79
-------- -
1.094
(0.115)
9.547
- -
Covariance Matrix of ETA
LABOR77
LABOR79
LABOR77
-------0.116
0.127
LABOR79
-------0.199
Panel Data model
Added error covariances:
FR TE 5 1 TE 6 2 TE 7 3 TE 8 4
PSI
Note: This matrix is diagonal.
LABOR77
-------0.116
(0.020)
5.935
LABOR79
-------0.060
(0.016)
3.721
Squared Multiple Correlations for Structural
Equations
LABOR77
-------- -
LABOR79
-------0.698
Panel data model Cdn. Quality of Life
1977-81
! Model for mean differences
SY='H:\QOL3WAVE\imputed_data.dsf'
SE
Q199D Q156C Q156D Q156B QD7B
QK16F QK16G QK16E /
MO NY=8 NE=2 LY=FU,FI PS=SY,FR
TE=SY BE=FU,FI TY=FR AL=FI
LE
LABOR77 LABOR79
VA 1.0 LY 1 1 LY 5 2
FR LY 2 1 LY 3 1 LY 4 1
FR LY 6 2 LY 7 2 LY 8 2
FR TE 5 1 TE 6 2 TE 7 3 TE 8 4
EQ TY 5 TY 1
EQ TY 6 TY 2
EQ TY 7 TY 3
EQ TY 8 TY 4
EQ LY 2 1 LY 6 2
EQ LY 3 1 LY 7 2
EQ LY 4 1 LY 8 2
FR AL 2
OU ME=ML MI SC ND=3
Panel Data model
Alternative specification with
stability coefficient:
PS=SY BE=SD
[or BE=FU,FI then FR BE 2 1]
Panel Data
ALPHA
LABOR77
-------- -
LABOR79
-------0.043
(0.014)
3.051
Higher score = pro-union (ref. indicator: too
much/too little power… too little=5 too
much=1
Panel Data
Panel data model Cdn. Quality of Life 1977-81
! Impact
of TV newspapers on labor union attitudes
SY='H:\QOL3WAVE\imputed_data.dsf'
SE
Q258 Q260 Q261 Q199D Q156C Q156D Q156B QD7B QK16F QK16G QK16E /
MO NY=11 NE=4 LY=FU,FI PS=SY TE=SY BE=FU,FI
LE
1
NEWSP TV LABOR77 LABOR79
TV
VA 1.0 LY 2 1
1
VA 1.0 LY 3 2
1 Newsp
1
FR LY 1 1
FI TE 3 3
VA 1.0 LY 4 3 LY 8 4
Union Atts
FR LY 5 3 LY 6 3 LY 7 3
1977
FR LY 9 4 LY 10 4 LY 11 4
1
FR BE 4 3
FR BE 3 2 BE 3 1
FR BE 4 2 BE 4 1
1
1
1
1
1
FR PS 2 1
FR TE 11 7 TE 10 6 TE 9 5 TE 8 4
OU ME=ML MI SC ND=3
1
Union atts
1979
1
1
1
1
Panel Data
LISREL Estimates (Maximum Likelihood)
LAMBDA-Y
Q258
NEWSP
-------0.917
(0.176)
5.212
TV
-------- -
LABOR77
-------- -
LABOR79
-------- -
Q260
1.000
- -
- -
- -
Q261
- -
1.000
- -
- -
Q199D
- -
- -
1.000
- -
Q156C
- -
- -
-1.891
(0.214)
-8.819
- -
Panel Data
BETA
NEWSP
TV
NEWSP
-------- - -
TV
-------- - -
LABOR77
0.061
(0.026)
2.325
-0.005
(0.011)
-0.406
LABOR79
0.047
(0.030)
1.584
-0.017
(0.014)
-1.216
LABOR77
-------- -
LABOR79
-------- -
- -
- -
- -
- -
1.081
(0.113)
9.564
- -
Panel Data
Panel data model Cdn. Quality of Life 1977-81
! Impact of TV newspapers on labor union attitudes
! Controls: education sex union membership
SY='H:\QOL3WAVE\imputed_data.dsf'
SE
Q258 Q260 Q261 Q199D Q156C Q156D Q156B QD7B QK16F QK16G QK16E Q63 SEX Q201 RAGE Q157/
MO NY=11 NE=4 LY=FU,FI PS=SY TE=SY BE=FU,FI NX=5 NK=5 FIXEDX
LE
NEWSP TV LABOR77 LABOR79
LK
MEMBER SEX EDUC AGE INCOME
VA 1.0 LY 2 1
VA 1.0 LY 3 2
FR LY 1 1
FI TE 3 3
VA 1.0 LY 4 3 LY 8 4
FR LY 5 3 LY 6 3 LY 7 3
FR LY 9 4 LY 10 4 LY 11 4
FR BE 4 3
FR BE 3 2 BE 3 1
FR BE 4 2 BE 4 1
FR PS 2 1
FR TE 11 7 TE 10 6 TE 9 5 TE 8 4
OU ME=ML MI SC ND=3
Panel Data
BETA
NEWSP
NEWSP
-------- -
TV
- -
TV
-------- - -
LABOR77
-------- -
LABOR79
-------- -
- -
- -
- -
- -
LABOR77
-0.025
(0.034)
-0.738
-0.012
(0.011)
-1.157
LABOR79
0.068
(0.042)
1.622
-0.010
(0.013)
-0.751
1.033
(0.115)
8.970
MEMBER
--------0.017
(0.039)
-0.422
SEX
-------0.011
(0.035)
0.311
EDUC
--------0.097
(0.009)
-11.303
AGE
--------0.014
(0.001)
-13.496
INCOME
--------0.014
(0.005)
-2.898
TV
-0.013
(0.070)
-0.182
-0.150
(0.062)
-2.408
0.025
(0.015)
1.685
-0.017
(0.002)
-9.807
0.001
(0.009)
0.113
LABOR77
0.286
(0.036)
7.880
-0.056
(0.026)
-2.131
-0.039
(0.008)
-5.158
-0.005
(0.001)
-5.331
-0.010
(0.004)
-2.557
LABOR79
0.045
(0.042)
1.082
0.114
(0.033)
3.487
0.001
(0.009)
0.069
0.001
(0.001)
0.966
-0.006
(0.004)
-1.436
- -
GAMMA
NEWSP
Another model (panel7)
BETA
INEQ77
LABOR77
INEQ77
-------- - -
LABOR77
-------- - -
INEQ79
-------- -
LABOR79
-------- -
- -
- -
INEQ79
0.704
(0.069)
10.214
0.012
(0.110)
0.105
- -
- -
LABOR79
-0.106
(0.044)
-2.400
0.819
(0.124)
6.622
- -
- -
Re-expressing parameters:
GROWTH CURVE MODELS
Intercept & linear (& sometimes quadratic)
terms
• Suitable for panel models with >2 waves
• Best for panel models with >3 waves
Linear Growth Model
Two Factor LGM
LISREL:
Parm1,
Intercept
Parm2,
Slope
1
0
1
2 manifest variable, 2 latent
variable model
LY matrix
1
0
0
V1 - t1
V2 - t2
1
0, 0
1
0, 0
INT Slope
V1
1
0
V2
1
1
TE matrix = elements equal
TY zero
PS matrix = SY,FR
AL free (“parm1” and “parm2”
above)
(parm1 in model = variance of
INT, parm2 = variance of Slope)
Linear Growth Model
Two Factor LGM
Parm1,
Intercept
Parm2,
Slope
1
0
1
1
0
0
V1 - t1
V2 - t2
1
0, 0
1
0, 0
Interpretation:
• intercept factor represents initial
status
•Slope factor represents difference
scores (V2-V1)
With single indicators, cannot estimate
error variances (as with any single
indicator SEM model)
Parm1 = mean intercept Parm2 = mean slope value
Linear Growth Model
Two Factor LGM
E.g., TV use, adolescents, hours/day
Parm1,
Intercept
Parm2,
Slope
1
0
1
Parm1 = 2.5
Parm2 = 1.0
Increase of 1 hour/day from t1 to t2
1
0
0
V1 - t1
V2 - t2
1
0, 0
1
0, 0
We will also get variances for the
Intercept and the Slope factors
Parm1 = mean intercept Parm2 = mean slope value
Some growth curve trajectories:
• Parallel stability
Some growth curve trajectories:
• Strict stability
Single-factor LGM
•Actually nested within 2 factor model
• take 2 factor model, intercept with 0 mean
and 0 variance or strictly proportional to
slope
Curve
1
V1
B1
V2
B1
V3
(can estimate var(e1),(e2),(e3) if
we impose constraint
v(e1)=v(e2)=v(e3) )
Not generally the best
model unless assumptions
met: (cf. Duncan et al. p.
31: when rank ordering of
individuals does not vary
across time despite mean
level changes)
Linear Growth Model
Two Factor LGM
Parm1,
Parm2,
Intercept
Slope
1
1
1
0
0
LV-t2
LV-t1
1
1
1
0,
0
A bit more complicated with
latent variables instead of single
manifest variables
1
0,
1
0,
1 1
1
0,
0,
0,
… but the same basic
principle.
Linear Growth Model
Two Factor Linear Growth Model
Parm1,
Parm2,
Intercept
LY matrix (LISREL)
Slope
1
0
1
1
2
1
0
t1
1
0,
0
t2
1
0,
0
Int
Slope
V1
1
0
V2
1
1
V3
1
2
t3
1
0,
*general test: vs. “unspecified growth model”
Same principle would apply
to k time points where k>3
More time points: test of
linearity of “growth”
(changes in mean)*
Unspecified 2 factor Growth Curve Model
Two Factor Unspecified Growth Model
Parm1,
Parm2,
Intercept
Slope
1
0
1
1
lambda
1
0
t1
1
0,
0
t2
1
0,
1 free lambda
parameter in LY
matrix
0
t3
1
0,
In k time-point model,
all but first 2 time
points are represented
by free parameters
3 factor Growth Curve Model
Parm1,
Intercept
Parm2,
Linear
1
0
1
1
Parm
3
0,
Quadratic
0
2
1
1
0
t1
1
0,
Non-linear growth
0
t2
1
0,
0
t3
1
0,
4
3 factor Growth Curve Model
Parm1,
Intercept
Parm2,
Linear
1
0
1
1
2
1
0,
INT LIN Quad
1
0
0
t2
1
0,
LY matrix
Quadratic
0
1
t1
0,
parm3
4
V1
1
0
0
V2
1
1
2
V3
1
2
4
0
t3
1
0,
TE is constrained to equality
across t’s
This is a “saturated” model
(perfect fit by definition)
PS is free
AL is free (parm1-3)
All TY elements 0
Examples:
Z:\baer\Week4Examples\LatentGrowth
Single variable models:
LGMProg1.ls8 (output=.out)
intercept model
LGMProg2.ls8 - single factor curve model
LGMProg3.ls8 - intercept + slope
LGMProg4.ls8 – intercept + slope +
quadratic
Where do “growth factors” fit into
models?
• Examination of predictors (antecedents)
and consequences of change
Two Factor Linear Growth Model
Parm1,
Note: Intercept-slope
covariance now
disturbance
covariance
Parm2,
Intercept
Slope
1
0
1
1
2
1
0
t1
PROGRAM
LGMProg5
1
0,
0
t2
1
0,
0
t3
1
0,
Consequences
Two Factor Linear Growth Model
Parm1,
Parm2,
Intercept
Slope
1
0
1
1
2
1
0
t1
1
0,
0
t2
1
0,
0
t3
1
0,
Model LGMProg6.ls8
Dependent variable: job satisfaction, wave 8.
Multiple indicators for the
variable(s) involved in growth
curves
• “factor of curves” LGM
• Intercept term and slope term (e.g.) constructed for each indicator
• if there are 3 variables & 4 waves, we will have an intercept term
based on 4 manifest variables representing time x 3 manifest
variables per time (3 intercept terms)
“common intercept” variable will have 3 indicators (intercept
terms)
“common slope” will have 3 indicators (slope terms)
common
intercept
1
x1-intercept
1
1
lambda2
lambda3
x2-Intercept
x3-intercept
111
1
1
x1-t3 x2-t3 x3-t3
x1-t1 x2-t1 x3-t1 x1-t2 x2-t2 x3-t2
1
1
1
1
1
1
1
1
1
Error variances now estimated (not constrained to
equality).. Could include corr. Errors too
common
intercept
1
lambda3
lambda2
1
1
x2-Intercept
x1-intercept
1
1
x3-intercept
1
1
1
x1-t2 x2-t2 x3-t2 x1-t3 x2-t3 x3-t3
x1-t1 x2-t1 x3-t1
0
1
10
2
x2-slope
x1-slope
2
1
1
1
1
x3-slope
lambda3a
lambda2a
common slope
1
Interactions
Easiest case: X1 is 0/1
X2 ix 0/1
Options: 1. Manually construct X3=X1*X2 outside
SEM software, estimate model with X1,X2,X3
exogenous. Test for interaction: fix regression coefficient
for X3 to 0.
2. Create two groups: X1=0 and X1=1. In each group,
X2 as exogenous variable. Test for interaction would be
H0: gamma[1] = gamma[2].
Extensions for X1, X2 >2 categories straightfoward (more
groups/dummy variables)
Interactions
Option 3: Model as a 4-group problem.
X1
1
0
X2 1
gr1 gr2
0
gr3 gr4
AL[1]=0 al[2], al[3],al[4] parameters to be
estimated.
Main effects model (no interaction) would allow for
al[2]≠al[3] ≠al[4] but pattern of differences would
be constrained such that…..
Interactions
Model as a 4-group problem.
X1
1
X2
1
gr1
0
gr3
0
gr2
gr4
AL[1]=0 al[2], al[3],al[4] parameters to be estimated.
Main effects model (no interaction) would allow for al[2]≠al[3] ≠al[4] but
pattern of differences would be constrained such that…..
The group1 vs. group 2 difference = group 3 vs. group 4 difference
(or group 1 vs. 3 difference = group 2 vs. group 4).
Programming in LISREL would be:
Al[1] – Al[2] = al[3]- al[4]
0 – al[2] = al[3] – al[4]
Al[2] = al[4]-al[3] LISREL: CO al 2 1 = al 4 1 – al 3 1
Test for interaction: run another model removing this constraint (all AL
completely free except group 1)
… more examples provided in text
Interactions
Interactions involving continuous variables.
Case 1: One continuous (single or multiple indicator) and one categorical variable
EASY: categorical variable becomes basis for grouping.
Group 1 Eta = gamma[1] Ksi + zeta
Group 2 Eta = gamma[2] Ksi + zeta
Test for interaction: H0: gamma[1] = gamma[2]
Case 2: Two continuous single indicator variables
Also somewhat straightforward:
Create single-indicator X3 = X2*X1
Case 3: Two continuous multiple indicator latent variables
This is not so easy! Substantial literature on this question
See course outline for extended list. (Schumacker and Mracoulides, eds.,
Interaction and Nonlinear Effects in Structural Equation Modeling).
Case 3A, not talked about much: X1 single indicator Ksi1 (X2, X3,X4)
Create: X1X2 , X1X3, X1,X4
Latent variable interactions
Major approaches:
• Kenny-Judd
• Simplified variants of Kenny-Judd,
modifications, etc. (Joreskog & Yang, 1996; Ping)
• Two-stage least squares (get instrumental
variables)
• Use SEM to estimate 2 factor model, save
latent variable “scores” (analogous to
factor scores), then use these
Latent variable interactions
• Use SEM to estimate 2 factor model, save latent
variable “scores” (analogous to factor scores),
then use these
In LISREL:
Mo nx=6 nk=2 lx=fu,fi ph-sy,fr td=sy
Va 1.0 lx 1 1 lx 4 2
Fr lx 2 1 lx 3 1 lx 5 2 lx 6 2
PS=Newfile.psf
OU
Latent variable interactions
•
Use SEM to estimate 2 factor model, save latent variable “scores”
(analogous to factor scores), then use these
In LISREL:
Mo nx=6 nk=2 lx=fu,fi ph-sy,fr td=sy
Va 1.0 lx 1 1 lx 4 2
Fr lx 2 1 lx 3 1 lx 5 2 lx 6 2
PS=Newfile.psf
OU
LISREL documentation suggests that a simple regression can be
estimated in PRELIS:
Sy=newfile.psf
ne inter=ksi1*ksi2
rg y on ksi1 ksi2 ksi1 ksi2
ou
Latent variable interactions
LISREL documentation suggests that a simple regression can be
estimated in PRELIS:
Sy=newfile.psf
ne inter=ksi1*ksi2
rg y on ksi1 ksi2 ksi1 ksi2
ou
…. But it should also be possible to a) construct “inter” (=ksi1*ksi2) and read
the 3 new “single indicator” variables back into LISREL for use with other
variables (including those which form the basis of multiple-indicator
endogenous variables.
If all else fails, construct a LISREL model for Ksi1, Ksi2, and put FS (factor
score regressions) on the OU line:
OU ME=ML FS MI ND=4
.. And use factor score regressions to compute estimated factor scores in any
stat package (incl. PRELIS)
Example:
INTERACTION MODEL WITH INTERACTION TERM CREATED EXTERNALLY
SINGLE INDICATORS FOR EXOGENOUS LVS INVOLVED IN INTERACTION
DA NO=1111 NI=10 MA=CM
CM FI=G:\ICPSR\INTERACTIONS\INT5b.COV FU FO
(10F10.7)
LABELS
lv1 lv2 interact
sex race v217 v216 v125 v127 v130
se
8 9 10 1 2 3 4 5 6 7/
mo ny=3 ne=1 LY=FU,FI PS=SY,FR TE=SY c
nx=7 nk=7 fixedx ga=fu,fr
va 1.0 ly 1 1
fr ly 2 1 ly 3 1
ou me=ml se tv mi sc
LISREL Estimates (Maximum Likelihood)
LAMBDA-Y
v125
ETA 1
-------1.00
v127
1.34
(0.24)
5.59
v130
0.65
(0.11)
5.74
Example:
Dep var = inequality att’s (high
score  “more individual effort”)
GAMMA
ETA 1
lv1
--------0.04
(0.06)
-0.65
lv2
--------0.21
(0.08)
-2.57
interact
-------0.85
(0.45)
1.89
sex
-------0.22
(0.11)
2.10
race
--------0.30
(0.13)
-2.27
GAMMA
ETA 1
v216
-------0.09
(0.03)
2.92
Lv1=relig. Lv2=econ. status
v217
-------0.05
(0.03)
1.75
Kenny-Judd model
Typically, literature (e.g., Kenny-Judd, 1984; Hayduk, 1987) starts with 2indicator example (2 LV’s each with 2 indicators).
Ksi1
Ksi2
Ksi1*Ksi2 (interaction term)
Indicators:
Ksi1:
x1
x2
Ksi2:
x3
x4
Possible product terms:
x1*x3
x1*x4
x2*X3 X2*x4
Kenny-Judd model use 4 product terms but Joreskog and Yang show that the
model can be constructed with 1 product term.
Kenny-Judd model
Typically, literature (e.g., Kenny-Judd, 1984; Hayduk, 1987) starts with 2-indicator example (2 LV’s
each with 2 indicators).
Ksi1
Ksi2
Ksi1*Ksi2 (interaction term)
Indicators: Ksi1:
x1
x2
Ksi2:
x3
x4
Possible product terms:
x1*x3
x1*x4
x2*X3
X2*x4
Kenny-Judd model use 4 product terms but Joreskog and Yang show that the
model can be constructed with 1 product term.
Kenny-Judd do not include constant intercept terms (alpha, tau).. But even if
dependent variable, Ksi1, Ksi2 and zeta have zero means, alpha will still be
nonzero. - means of observed variables functions of other parameters in
the model and therefore intercept terms have to be included.
- Nonnormality even if x’s are normal (ADF estimation often recommended if
sample size acceptable)
Kenny-Judd model
Kenny-Judd model
alpha=1 term
Kenny-Judd model, mod.
INTERACTION MODEL KENNY JUDD MODIFICATION (JORESKOG AND YANG)
ONE INTERACTION INDICATOR 3 INDICATORS PER L.V.
DA NO=1111 NI=22
CM FI=G:\ICPSR2000\INTERACTIONS\INT5c.COV FU FO
(22F20.11)
ME FI=G:\ICPSR2000\INTERACTIONS\INT5C.MN FO
(22F20.11)
LABELS
v181 v9 v190 v221 v226 v227
relinc1 relinc2 relinc3 relinc4 relinc5
relinc6 relinc7 relinc8 reling9
sex race v217 v216 v125 v127 v130
se
20 21 22 1 2 3 4 5 6 9 16 17 18 19/
mo ny=3 ne=1 NX=11 NK=7 LY=FU,FI PS=SY,FR C
TE=SY TX=FR KA=FI C
LX=FU,FI GA=FU,FR PH=SY,FR TD=SY AL=FI TY=FR
va 1.0 ly 1 1
fr ly 2 1 ly 3 1
FI PH 3 1 PH 3 2
FR KA 3
VA 1.0 LX 1 1 LX 4 2 LX 7 3 LX 8 4 LX 9 5 LX 10 6 LX 11 7
FR TD 1 1 TD 2 2 TD 3 3 TD 4 4 TD 5 5 TD 6 6 TD 7 7
FR LX 2 1 LX 3 1 LX 5 2 LX 6 2 LX 7 1 LX 7 2
CO LX(7,1)=TX(1)
CO LX(7,2)=TX(4)
CO KA(3) = PH(2,1)
FI PH 3 1 PH 3 2
CO PH(3,3) = PH(1,1)*PH(2,2) + PH(2,1)**2
CO TX(6) = TX(1)*TX(4)
FI TD(8,8) TD(9,9) TD(10,10) TD(11,11)
CO TD(7,7) = TX(1)**2*TD(3,3) + TX(4)**2*TD(1,1) + PH(1,1)*TX(4) + C
PH(2,2)*TX(1) + TD(1,1)*TD(4,4)
OU ME=ML SE TV ND=3 AD=off
Kenny-Judd model, modified Joreskog/Yang
Parameter Specifications
LAMBDA-Y
ETA 1
-------0
1
2
v125
v127
v130
LAMBDA-X
v181
v9
v190
v221
v226
v227
relinc3
sex
race
v217
v216
KSI 1
-------0
3
4
0
0
0
Constr'd
0
0
0
0
KSI 2
-------0
0
0
0
5
6
Constr'd
0
0
0
0
KSI 3
-------0
0
0
0
0
0
0
0
0
0
0
KSI 4
-------0
0
0
0
0
0
0
0
0
0
0
KSI 5
-------0
0
0
0
0
0
0
0
0
0
0
KSI 6
-------0
0
0
0
0
0
0
0
0
0
0
Kenny-Judd model, modified Joreskog/Yang
GAMMA
ETA 1
KSI 1
--------0.023
(0.009)
-2.557
GAMMA
ETA 1
KSI 7
-------0.080
(0.029)
2.735
KSI 2
--------0.003
(0.015)
-0.198
KSI 3
--------0.008
(0.004)
-1.984
KSI 4
-------0.209
(0.098)
2.130
KSI 5
--------0.324
(0.125)
-2.593
KSI 6
-------0.051
(0.024)
2.094